Classical epidemiology has mainly focused on idealized homogeneous network structures such as complete graphs or networks where each person has about the same number of contacts.
However, a more detailed look at how changes in the contact network topology will affect the spread of an epidemic is necessary. To gain insights into methods for effectively slowing down the spread of the virus in the network, it will be useful to conduct a study into the sensitivity of the rate of spread of the virus to the topology of the network. The existing literature on this topic is mainly focused on asymptotical analysis [1]}, i.e. asymptotically large populations, or the early stage of the spread of an epidemic, where the reduction of the largest eigenvalue of the contact network (adjacency matrix) plays a crucial role [2]}, [3]}. However, once an epidemic is already spread out across a network, other dynamics need to be taken into account. This topic, however, received relatively small attention in the literature [1]} and the results are mainly based on time-discrete models [5]}, [6]} which may not consider the continuous the important aspect of time in a statistical sound way, or on continuous-time differential equation models that do not take the network structure into account.
